This paper presents a comprehensive study on the evolution of the small-strain shear modulus (G) of granular materials during hydrostatic compression, conventional triaxial, reduced triaxial, and p-constant triaxial tests using 3D discrete element method. Results from the hydrostatic compression tests indicate that G can be precisely estimated using Hardin's equation and that a linear correlation exists between a stress-normalized G and a function of mechanical coordination number and void ratio. During the triaxial tests, the specimen fabric, which refers to the contact network within the particle assembly, remains almost unchanged within a threshold range of stress ratio (SR). The disparity between measured G and predicted G, as per empirical equations, is less than 10% within this range. However, once this threshold range is exceeded, G experiences a significant SR effect, primarily due to considerable adjustments in the specimen's fabric. The study concludes that fabric information becomes crucial for accurate G prediction when SR threshold is exceeded. A stiffness-stress-fabric relationship spanning a wide range of SR is put forward by incorporating the influences of redistribution of contact forces, effective connectivity of fabric, and fabric anisotropy into the empirical equation.

Granular soil generally exhibits an anisotropic stiffness in engineering but challenging to quantify in situ and laboratory condition, due to a lack of the appropriate factor and quantitative research. In this paper, discrete element method is employed to create two typical types of soil fabric and conduct shear wave measurement in double direction, with the microscopic parameters monitored to investigate the connection with macroscopic stiffness anisotropy. The results show that the reference fabric increases as fabric anisotropy increases first and then decreases with further increase in the XZ stress plane, while always decreases approximately linearly in the XY stress plane. The reference fabric is determined by the contact density in the direction of wave propagation and particle perturbation under microscale examination. The results also reveal a linear relationship between the macroscopic stiffness anisotropy and microscopic fabric anisotropy, which could be used as an effective method to reflect the degree of anisotropy in situ by wave measurement. And the applicability of the expression of small-strain shear modulus is also discussed.

The small-strain shear modulus and shear strength are mechanical parameters crucial in the design of geotechnical structures and in the analyses of soil-structure interactions. This paper proposes a new approach for estimating these mechanical parameters. The proposed approach is predicated on the proportional inverse relationship of mechanical soil properties to the soil-water characteristic curve. The proposed equations supporting the approach incorporate a scaling function, alongside the initial saturated mechanical property. The performance of the proposed equations was demonstrated across a variety of soil textures, utilizing literature soils subjected to varying net normal stresses, and across a wide range of matric suction up to the residual suction zone. It was established that a correlation existed between the scaling function and air-entry value for both small-strain shear modulus and shear strength of unsaturated soils. In addition, the behavior of the scaling function under potential hysteretic effects was demonstrated and recommendations were provided on how to apply the proposed model under such conditions. Finally, the modified equations including the correlation for the scaling function were used to predict additional literature soils.

Incorporation of nonplastic fines can dramatically affect the liquefaction resistance and stiffness of sands. This study aims to evaluate the influence of nonplastic fines on the liquefaction resistance and small-strain shear modulus of calcareous sand under cyclic loading. Forty-seven sets of undrained cyclic triaxial tests and companion bender element tests are conducted on reconstituted specimens. The cyclic behavior of clean sand and silty sand with varying fines content is examined with respect to the global void ratio, relative density, and granular skeleton void ratio. The findings demonstrate that the microscopic contacts between coarse and fine grains have a significant impact on the macroscopic behavior of sand-fines mixtures. The experimental findings are evaluated using the equivalent granular skeleton void ratio, which has been recognized as a suitable parameter to describe the overall effect of fines. The findings on calcareous sand with fines are supplemented and compared with published data in accordance with the semiempirical simplified approach for liquefaction triggering based on shear wave velocity.

In recent years, several empirical and semiempirical relationships have been proposed to predict the small-strain shear modulus of unsaturated fine-grained soils along different hydraulic and mechanical loadings paths. However, a major deficiency of these relationships is the absence of a coupled linkage between hydraulic and mechanical processes that occur in unsaturated conditions. Specifically, the void ratio and effective stress are considered uncoupled, and changes in soil volume are rarely considered when implementing soil water retention curves in these equations. This study aims to address these deficiencies by discussing the coupled effect of hydraulic and mechanical processes in unsaturated soils and presenting a semiempirical model to predict the small-strain shear modulus, Gmax, of unsaturated low plasticity soils subjected to volume and effective stress changes along different mechanical and hydraulic stress paths. Predictions from this model and three other recently proposed models in the literature are compared with experimental results obtained from a series of suction-controlled bender element tests on silty soil specimens to validate the proposed model. The comparison reveals that the model proposed in this study provides more consistent predictions of the small-strain shear modulus during hydraulic hysteresis, as well as different paths of loading and unloading.